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Recent questions and answers in Engineering Mathematics
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votes
0
answers
1
GATE2020-CE-1-1
In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$ ... The above equation is a second order linear equation a second degree linear equation a second order non-linear equation a second degree non-linear equation
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-1
partial-differential-equation
engineering-mathematics
0
votes
0
answers
2
GATE2020-CE-1-2
The value of $\lim_{x\to\infty}\dfrac{x^2-5x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-1
engineering-mathematics
limit
calculus
0
votes
0
answers
3
GATE2020-CE-1-3
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round off to the nearest integer), is $35$ $48$ $69$ $84$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-1
engineering-mathematics
linear-algebra
linear-interpolation
0
votes
0
answers
4
GATE2020-CE-1-4
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-1
engineering-mathematics
0
votes
0
answers
5
GATE2020-CE-1-18
The probability that a $50$ year flood may $\textbf{NOT}$ occur at all during $25$ years life of a project (round off to two decimal places), is _______.
asked
Feb 28, 2020
in
Probability and Statistics
by
jothee
(
2.7k
points)
gate2020-ce-1
probability-and-statistics
engineering-mathematics
probability
numerical-answers
0
votes
0
answers
6
GATE2020-CE-1-26
For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the solution is $-5e^{2t}+6e^{3t}$ $5e^{2t}+6e^{3t}$ $-10e^{2t}+10e^{3t}$ $10e^{2t}+10e^{3t}$
asked
Feb 28, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-1
ordinary-differential-equation
engineering-mathematics
0
votes
0
answers
7
GATE2020-CE-1-27
A continuous function $f(x)$ is defined. If the third derivative at $x_i$ is to be computed by using the fourth order central finite-divided-difference scheme (with step length $=h$ ...
asked
Feb 28, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-1
calculus
functions
engineering-mathematics
0
votes
0
answers
8
GATE2020-CE-1-39
If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral $\int_C [(y+z)dx+(x+z)dy+(x+y)dz] $ is ______
asked
Feb 28, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-1
calculus
engineering-mathematics
integrals
numerical-answers
0
votes
0
answers
9
GATE2020-CE-1-40
Consider the system of equations $\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 2 \\ 1 \end{bmatrix}$ The value of $x_3$(round off to the nearest integer), is ___________.
asked
Feb 28, 2020
in
Linear Algebra
by
jothee
(
2.7k
points)
gate2020-ce-1
matrix-algebra
linear-algebra
engineering-mathematics
numerical-answers
0
votes
0
answers
10
GATE2020 CE-2-1
The ordinary differential equation $\dfrac{d^2u}{dx^2}$- 2x^2u +\sin x = 0$ is linear and homogeneous linear and nonhomogeneous nonlinear and homogeneous nonlinear and nonhomogeneous
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-2
ordinary-differential-equation
engineering-mathematics
0
votes
0
answers
11
GATE2020 CE-2-2
The value of $\lim_{x\to\infty}\dfrac{\sqrt{9x^2+2020}}{x+7}\:\text{is}$ $\dfrac{7}{9}$ $1$ $3$ indeterminable
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-2
engineering-mathematics
differential-equations
0
votes
0
answers
12
GATE2020 CE-2-3
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson's rules with a common step size. In this context, which one of the following ... NON-zero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
asked
Feb 13, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-2
calculus
engineering-mathematics
integrals
0
votes
0
answers
13
GATE2020 CE-2-4
The following partial differential equation is defined for $u:u (x,y)$ $\dfrac{\partial u}{\partial y}=\dfrac{\partial^2 u}{\partial x^2}; \space y\geq0; \space x_1\leq x \leq x_2$ The set of auxiliary ... the equation uniquely, is three initial conditions three boundary conditions two initial conditions and one boundary condition one initial condition and two boundary conditions
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-2
partial-differential-equation
engineering-mathematics
0
votes
0
answers
14
GATE2020 CE-2-18
A fair (unbiased) coin is tossed $15$ times. The probability of getting exactly $8$ Heads (round off to three decimal places), is _______.
asked
Feb 13, 2020
in
Probability and Statistics
by
jothee
(
2.7k
points)
gate2020-ce-2
numerical-answers
probability-and-statistics
engineering-mathematics
probability
0
votes
0
answers
15
GATE2020 CE-2-24
Velocity distribution in a boundary layer is given by $\dfrac{u}{U_\infty} = \sin\large \left( \dfrac{\pi}{2}\dfrac{y}{\delta} \right)$, where $u$ is the velocity at vertical coordinate $y,\: U_\infty$ is the free stream velocity and $\delta$ is the boundary layer ... $\ s^{-1}$, round off to two decimal places) at $y = 0$, is ________.
asked
Feb 13, 2020
in
Calculus
by
jothee
(
2.7k
points)
gate2020-ce-2
numerical-answers
calculus
engineering-mathematics
gradient
0
votes
0
answers
16
GATE2020 CE-2-26
An ordinary differential equation is given below $6\dfrac{d^2y}{dx^2}+\frac{dy}{dx}-y=0$ The general solution of the above equation (with constants $C_1$ and $C_2$), is $y(x) = C_1e^\frac{-x}{3} + C_2e^\frac{x}{2}$ $y(x) = C_1e^\frac{x}{3} + C_2e^\frac{-x}{2}$ $ y(x) = C_1xe^\frac{-x}{3} + C_2e^\frac{x}{2}$ $ y(x) = C_1e^\frac{-x}{3} + C_2xe^\frac{x}{2}$
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-2
ordinary-differential-equation
engineering-mathematics
0
votes
0
answers
17
GATE2020 CE-2-27
A $4 \times 4$ matrix $[P]$ is given below $[P] = \begin{bmatrix}0 &1 &3 &0 \\-2 &3 &0 &4 \\0 &0 &6 &1 \\0 &0 &1 &6 \end{bmatrix}$ The eigen values of $[P]$ are $0, 3, 6, 6$ $1, 2, 3, 4$ $3, 4, 5, 7$ $1, 2, 5, 7$
asked
Feb 13, 2020
in
Linear Algebra
by
jothee
(
2.7k
points)
gate2020-ce-2
matrix-algebra
linear-algebra
engineering-mathematics
0
votes
0
answers
18
GATE2020 CE-2-39
The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by $ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \sin nx$ The value of $a_0$(round off to two decimal places), is ________.
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-2
numerical-answers
partial-differential-equation
engineering-mathematics
0
votes
0
answers
19
GATE2020 CE-2-40
The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The absolute error in the computed volume ( in $cm^3$ ,round off to three decimal places), is ________
asked
Feb 13, 2020
in
Engineering Mathematics
by
jothee
(
2.7k
points)
gate2020-ce-2
numerical-answers
engineering-mathematics
+2
votes
1
answer
20
GATE2019 CE-1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=1$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ ... $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})= \infty$
answered
Jan 17, 2020
in
Calculus
by
KUSHAGRA गुप्ता
(
140
points)
gate2019-ce-1
calculus
limit
engineering-mathematics
0
votes
0
answers
21
GATE2017 CE-2-1
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants): $3x_1+2x_2=c_1$ $4x_1+x_2=c_2$ The characteristic equation for these simultaneous equation is $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
asked
Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017-ce-2
engineering-mathematics
equations
0
votes
0
answers
22
GATE2017 CE-2-2
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
asked
Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017-ce-2
engineering-mathematics
partial-differential-equation
0
votes
0
answers
23
GATE2017 CE-2-19
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
asked
Aug 7, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017-ce-2
vector-calculus
divergence
numerical-answers
calculus
engineering-mathematics
0
votes
0
answers
24
GATE2017 CE-2-20
A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the coin is tossed one more time, the probability (up to one decimal place) of obtaining H again, given the previous realizations of H, H and H, would be ________
asked
Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017-ce-2
numerical-answers
engineering-mathematics
0
votes
0
answers
25
GATE2017 CE-2-26
The tangent to the curve represented by $y=x \text{ ln }x$ is required to have $45^{\circ}$ inclination with the $x$-axis. The coordinates of the tangent point would be $(1,0)$ $(0, 1)$ $(1,1)$ $(\sqrt{2}, (\sqrt{2})$
asked
Aug 7, 2019
in
Engineering Mathematics
by
gatecse
(
3.9k
points)
gate2017-ce-2
engineering-mathematics
tangent-point
0
votes
0
answers
26
GATE2017 CE-2-27
Consider the following definite integral: $I= \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
asked
Aug 7, 2019
in
Calculus
by
gatecse
(
3.9k
points)
gate2017-ce-2
definite
integral
calculus
engineering-mathematics
0
votes
0
answers
27
GATE2017 CE-2-28
If $A = \begin{bmatrix} 1 & 5 \\ 6 & 2 \end{bmatrix}$ and $B= \begin{bmatrix} 3 & 7 \\ 8 & 4 \end{bmatrix}, \: AB^T$ is equal to $\begin{bmatrix} 38 & 28 \\ 32 & 56 \end{bmatrix}$ $\begin{bmatrix} 3 & 40 \\ 42 & 8 \end{bmatrix}$ $\begin{bmatrix} 43 & 27 \\ 34 & 50 \end{bmatrix}$ $\begin{bmatrix} 38 & 32 \\ 28 & 56 \end{bmatrix}$
asked
Aug 7, 2019
in
Linear Algebra
by
gatecse
(
3.9k
points)
gate2017-ce-2
matrix
linear-algebra
engineering-mathematics
0
votes
0
answers
28
GATE2017 CE-2-29
Consider the following second-order differential equation: $y’’ – 4y’+3y =2t -3t^2$. The particular solution of the differential solution equation is $ – 2 -2t-t^2$ $ – 2t-t^2$ $2t-3t^2$ $ – 2 -2t-3 t^2$
asked
Aug 7, 2019
in
Partial Differential Equation (PDE)
by
gatecse
(
3.9k
points)
gate2017-ce-2
differential-equation
particular-solution
engineering-mathematics
0
votes
2
answers
29
GATE2019 CE-2: 43
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \: 1.87$, and $1.15 \:m$. The area (in $m^2$, round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is ________
answered
Feb 20, 2019
in
Numerical Methods
by
moinkhan
(
140
points)
gate2019-ce-2
numerical-methods
numerical-answers
engineering-mathematics
+1
vote
0
answers
30
GATE2019 CE-1: 2
Consider a two-dimensional flow through isotropic soil along $x$ direction and $z$ direction. If $h$ is the hydraulic head, the Laplace's equation of continuity is expressed as $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...
asked
Feb 14, 2019
in
Partial Differential Equation (PDE)
by
Arjun
(
2.8k
points)
gate2019-ce-1
laplace-equation
continuity
partial-differential-equation
engineering-mathematics
+1
vote
0
answers
31
GATE2019 CE-1: 3
A simple mass-spring oscillatory system consists of a mass $m$, suspended from a spring of stiffness $k$. Considering $z$ as the displacement of the system at any time $t$, the equation of motion for the free vibration of the system is $m \ddot{z} + kz = 0$. The natural frequency of the system is $\dfrac{k}{m} \\$ $\sqrt{ \dfrac{k}{m}} \\$ $\dfrac{m}{k}\\$ $\sqrt{ \dfrac{m}{k}}$
asked
Feb 14, 2019
in
Engineering Mathematics
by
Arjun
(
2.8k
points)
gate2019-ce-1
engineering-mathematics
+1
vote
0
answers
32
GATE2019 CE-1: 4
For a small value of $h$, the Taylor series expansion for $f(x+h)$ is $f(x)+h{f}' (x) + \dfrac{h^2}{2!}{f}''(x) + \dfrac{h^3}{3!}{f}'''(x)+\dots \infty \\$ $f(x)-h{f}' (x) + \dfrac{h^2}{2!}{f}''(x) - \dfrac{h^3}{3!}{f}'''(x)+ \dots \infty \\$ ... $f(x)-h{f}' (x) + \dfrac{h^2}{2}{f}''(x) - \dfrac{h^3}{3}{f}'''(x)+ \dots \infty $
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019-ce-1
taylor-series
calculus
engineering-mathematics
0
votes
0
answers
33
GATE2019 CE-1: 23
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flood event (in years, round off to $1$ decimal place is ________
asked
Feb 14, 2019
in
Probability and Statistics
by
Arjun
(
2.8k
points)
gate2019-ce-1
probability
numerical-answers
probability-and-statistics
engineering-mathematics
0
votes
0
answers
34
GATE2019 CE-1: 26
Which one of the following is NOT a correct statement? The function $\sqrt[x]{x}, \: (x>0)$, has the global maxima at $x=e$ The function $\sqrt[x]{x}, \: (x>0)$, has the global minima at $x=e$ The function $x^3$ has neither global minima nor global maxima The function $\mid x \mid$ has the global minima at $x=0$
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019-ce-1
maxima-minima
calculus
engineering-mathematics
0
votes
0
answers
35
GATE2019 CE-1: 27
A one-dimensional domain is discretized into $N$ sub-domains of width $\Delta x$ with node numbers $i=0,1,2,3, \dots , N$. If the time scale is discretized in steps of $\Delta t$, the forward-time and centered-space finite difference approximation at i th node and n th time step, for the ...
asked
Feb 14, 2019
in
Probability and Statistics
by
Arjun
(
2.8k
points)
gate2019-ce-1
probability-and-statistics
engineering-mathematics
discrete-random-variables
0
votes
0
answers
36
GATE2019 CE-1: 30
Consider two functions: $x=\psi \text{ ln } \phi$ and $y= \phi \text{ ln } \psi$. Which one of the following is the correct expression for $\frac{\partial \psi}{\partial x}$? $\dfrac{x \: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi -1} \\$ ... $\dfrac{\: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi -1}$
asked
Feb 14, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019-ce-1
calculus
engineering-mathematics
functions
0
votes
0
answers
37
GATE2019 CE-1: 44
Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round off to $1$ decimal place), is _________
asked
Feb 14, 2019
in
Ordinary Differential Equation (ODE)
by
Arjun
(
2.8k
points)
gate2019-ce-1
differential-equation
numerical-answers
engineering-mathematics
0
votes
0
answers
38
GATE2019 CE-2: 1
Euclidean norm (length) of the vector $\begin{bmatrix} 4 & -2 & -6 \end{bmatrix}^T$ is $\sqrt{12}$ $\sqrt{24}$ $\sqrt{48}$ $\sqrt{56}$
asked
Feb 12, 2019
in
Linear Algebra
by
Arjun
(
2.8k
points)
gate2019-ce-2
matrix-algebra
linear-algebra
engineering-mathematics
0
votes
0
answers
39
GATE2019 CE-2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2-a^2} \\$ $\dfrac{s}{s^2+a^2}$
asked
Feb 12, 2019
in
Engineering Mathematics
by
Arjun
(
2.8k
points)
gate2019-ce-2
ordinary-differential-equation
engineering-mathematics
laplace-transform
0
votes
0
answers
40
GATE2019 CE-2: 3
The following inequality is true for all $x$ close to $0$. $2-\dfrac{x^2}{3} < \dfrac{x \sin x}{1- \cos x} <2$ What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$? $0$ $1/2$ $1$ $2$
asked
Feb 12, 2019
in
Calculus
by
Arjun
(
2.8k
points)
gate2019-ce-2
limit
calculus
engineering-mathematics
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